Approach to criticality in sandpiles
Name
Fey-2010-Approach to critical.pdf
Size
576.86 KB
Format
Adobe PDF
Checksum (MD5)
a8b905497c23f9e642ac41c1d7d7e7c5
Author(s)
Levine, Lionel
Fey, Anne
Wilson, David B.
Date Issued
September 2010
Journal
Physical Review E
Publisher
American Physical Society
Citation
Fey, Anne, Lionel Levine, and David B. Wilson. “Approach to criticality in sandpiles.” Physical Review E 82.3 (2010): 031121. © 2010 The American Physical Society.
Version
Final published version
Abstract
A popular theory of self-organized criticality predicts that the stationary density of the Abelian sandpile model equals the threshold density of the corresponding fixed-energy sandpile. We recently announced that this “density conjecture” is false when the underlying graph is any of Z2, the complete graph Kn, the Cayley tree, the ladder graph, the bracelet graph, or the flower graph. In this paper, we substantiate this claim by rigorous proof and extensive simulations. We show that driven-dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink. Nevertheless, we do find (and prove) a relationship between the two models: the threshold density of the fixed-energy sandpile is the point at which the driven-dissipative sandpile begins to lose a macroscopic amount of sand to the sink.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.82.031121
